opgave 10 oef 2 exponential smoothing inschrijving personenwagens. umran celik

*Unverified author*

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 18:00:12 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem.htm/, Retrieved Mon, 08 Jun 2009 02:01:06 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

580 579 572 560 551 537 541 588 607 599 578 563 566 561 554 540 526 512 505 554 584 569 540 522 526 527 516 503 489 479 475 524 552 532 511 492 492 493 481 462 457 442 439 488 521 501 485 464 460 467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.562890117745326 beta 0.154656619933915 gamma 0.776809761193287 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 566 577.284722222222 -11.2847222222224 14 561 565.620730231435 -4.62073023143523 15 554 554.763910604782 -0.7639106047817 16 540 538.844887969688 1.15511203031224 17 526 524.731622123252 1.26837787674833 18 512 511.250864069776 0.749135930223645 19 505 512.709712313483 -7.70971231348324 20 554 552.610991911792 1.38900808820767 21 584 569.921437633817 14.0785623661826 22 569 568.683646174791 0.316353825209148 23 540 547.018450278338 -7.0184502783377 24 522 526.821910005568 -4.8219100055685 25 526 522.068602797306 3.93139720269426 26 527 521.054200118192 5.94579988180806 27 516 518.196449047451 -2.19644904745087 28 503 502.739647337086 0.260352662914386 29 489 488.700273022805 0.299726977195405 30 479 474.952719296432 4.04728070356828 31 475 476.137724903373 -1.13772490337323 32 524 524.141791723735 -0.141791723734968 33 552 546.080054557132 5.9199454428682 34 532 536.047373222968 -4.04737322296751 35 511 509.525943624173 1.47405637582733 36 492 495.685508668418 -3.68550866841815 37 492 495.472915080809 -3.47291508080895 38 493 491.258959391848 1.74104060815216 39 481 483.187904618284 -2.18790461828382 40 462 468.489090665015 -6.4890906650146 41 457 449.995288504688 7.00471149531182 42 442 441.209488563907 0.790511436093254 43 439 438.432296730543 0.567703269456729 44 488 487.514548846835 0.485451153164888 45 521 511.698801498316 9.30119850168381 46 501 500.313983495562 0.686016504438442 47 485 478.872808758883 6.12719124111743 48 464 466.845786380568 -2.84578638056831 49 460 468.19729790819 -8.19729790818974 50 467 463.702406520997 3.29759347900307 51 460 455.91691471081 4.08308528919019 52 448 444.576897952211 3.42310204778857 53 443 438.396702870293 4.60329712970696 54 436 428.092371641874 7.90762835812563 55 431 431.808498521782 -0.808498521782383 56 484 482.531185348927 1.46881465107339 57 510 512.790981695035 -2.79098169503459 58 513 493.150238761464 19.8497612385362 59 503 487.48793720496 15.5120627950404 60 471 481.658010883794 -10.6580108837944 61 471 480.076125558585 -9.0761255585847 62 476 482.194288543984 -6.19428854398382 63 475 471.710945409185 3.28905459081528 64 470 462.00907496953 7.99092503047007 65 461 461.507645838878 -0.507645838877579 66 455 451.710320362695 3.28967963730537 67 456 451.727379268286 4.27262073171414 68 517 508.385678878754 8.61432112124561 69 525 544.145477438642 -19.1454774386422 70 523 524.487193281545 -1.48719328154527 71 519 504.984729111186 14.0152708888141 72 509 488.938959183443 20.0610408165567 73 512 507.372659187999 4.62734081200085 74 519 521.562853780641 -2.56285378064138 75 517 520.039778076327 -3.03977807632668 76 510 511.517129536238 -1.51712953623803 77 509 505.095423045566 3.90457695443445 78 501 501.772598073284 -0.772598073283518 79 507 502.184676938404 4.81532306159608 80 569 563.01780987215 5.98219012784955 81 580 590.03611688648 -10.0361168864803 82 578 584.460288781853 -6.46028878185257 83 565 569.948462752511 -4.94846275251086 84 547 546.156225096548 0.843774903451617 85 555 547.734413280025 7.26558671997498 86 562 560.400111681626 1.59988831837416 87 561 560.852548961944 0.147451038056374 88 555 554.712727410285 0.287272589715030 89 544 551.376479813433 -7.37647981343298 90 537 539.362281843572 -2.36228184357162 91 543 539.885302340917 3.11469765908271 92 594 599.117707236083 -5.11770723608333 93 611 612.44298398353 -1.44298398352976 94 613 611.660422746748 1.33957725325195 95 611 601.473521940319 9.5264780596807 96 594 588.477073522251 5.52292647774937 97 595 595.958212719471 -0.958212719470794 98 591 602.443669385527 -11.4436693855271 99 589 594.297985819751 -5.29798581975149 100 584 583.903553214349 0.0964467856509827 101 573 576.604137836547 -3.60413783654667 102 567 567.490813657033 -0.490813657033186 103 569 570.164782978349 -1.16478297834851 104 621 623.058241317121 -2.05824131712086 105 629 638.485012763114 -9.48501276311413 106 628 632.551993596952 -4.55199359695166 107 612 619.747267657183 -7.74726765718276 108 595 592.083036876764 2.91696312323563 109 597 592.084614233413 4.91538576658729 110 593 595.015223981243 -2.01522398124337 111 590 591.783596033258 -1.78359603325805 112 580 583.025111488851 -3.02511148885139 113 574 570.266364095465 3.73363590453494 114 573 564.533621165878 8.46637883412166 115 573 570.993511959947 2.00648804005334 116 620 624.61759998127 -4.61759998127036 117 626 635.108087678417 -9.10808767841718 118 620 630.12118498376 -10.1211849837600 119 588 611.670769216 -23.6707692159998 120 566 575.852306177444 -9.85230617744355 121 557 565.421026998575 -8.4210269985748 122 561 553.406679702836 7.59332029716415 123 549 551.413999630308 -2.41399963030847 124 532 537.575973156142 -5.5759731561418 125 526 521.151111546567 4.84888845343323 126 511 513.225029526732 -2.2250295267321 127 499 506.114518842905 -7.11451884290454 128 555 546.202389126884 8.79761087311567 129 565 557.734396870765 7.26560312923539 130 542 558.060471976212 -16.0604719762122 131 527 527.589457089726 -0.589457089726466 132 510 507.387993626657 2.61200637334269 133 514 503.476503227935 10.5234967720652 134 517 508.230499698242 8.76950030175811 135 508 504.271241317975 3.72875868202453 136 493 494.121376006402 -1.12137600640199 137 490 485.435646356936 4.56435364306395 138 469 476.614583647384 -7.61458364738417 139 478 466.008066852632 11.9919331473678 140 528 525.115012099064 2.8849879009357 141 534 535.145205022292 -1.14520502229232 142 518 524.430859087689 -6.43085908768876 143 506 507.086100147311 -1.08610014731079 144 502 490.101546930038 11.8984530699624 145 516 497.321495401721 18.6785045982786 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 146 509.998058714981 496.139657338332 523.856460091631 147 502.555284399856 486.026979372301 519.08358942741 148 491.499401708899 472.069960130277 510.928843287521 149 488.312834222588 465.775725346407 510.849943098768 150 475.327174772423 449.494054843463 501.160294701384 151 478.867139664298 449.563545768332 508.170733560265 152 530.290606951614 497.353031824949 563.22818207828 153 539.236197152081 502.510037617764 575.962356686397 154 529.379206357434 488.717277962108 570.04113475276 155 520.036451135329 475.297880258004 564.775022012653 156 510.734041243188 461.783416191436 559.68466629494 157 515.184694152273 461.891398925546 568.477989378999

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem/1e73p1244419206.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem/1e73p1244419206.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem/2ai7h1244419206.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem/2ai7h1244419206.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem/31uec1244419206.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444192660ptoqdxd84v6wem/31uec1244419206.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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